Problem: Solve for $x$ and $y$ using elimination. ${x-4y = -9}$ ${-x-5y = -27}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the top and bottom equations together. $-9y = -36$ $\dfrac{-9y}{{-9}} = \dfrac{-36}{{-9}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {x-4y = -9}\thinspace$ to find $x$ ${x - 4}{(4)}{= -9}$ $x-16 = -9$ $x-16{+16} = -9{+16}$ ${x = 7}$ You can also plug ${y = 4}$ into $\thinspace {-x-5y = -27}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(4)}{= -27}$ ${x = 7}$